Emilian Parau | University of East Anglia (original) (raw)

Papers by Emilian Parau

Journal of Fluid Mechanics, Apr 13, 2018

Slender liquid jets that have a curved trajectory have been examined in a range of papers using a... more Slender liquid jets that have a curved trajectory have been examined in a range of papers using a method introduced in Wallwork et al. (2000, 2002) and Decent et al. (2002), for jets that emerge from an orifice on the surface of a rotating cylindrical container, successfully comparing computational results to measurements arising from laboratory experiments. Wallwork et al. (2000, 2002) and Decent et al. (2002) based their analysis on the slenderness of the jet, and neglected the torsion of the centreline of the jet which is valid since in most situations examined the torsion is zero or small. Shikhmurzaev & Sisoev (2017) used differential geometry and incorporated the torsion. This paper shows these two methods produce identical results at leading-order when the torsion is zero or when the torsion is O(1), in an asymptotic framework based upon the slenderness of the jet, and shows that the method of Wallwork et al. (2000, 2002) and Decent et al. (2002) is accurate for parameters corresponding to scenarios previously examined and also when the torsion is O(1). It is shown that the method of Shikhmurzaev & Sisoev (2017) should be used when the torsion is asymptotically large or when the jet is not slender.

Geophysical Research Letters

• Internal solitary waves in partially ice-covered water are generated in the laboratory. • Inter... more • Internal solitary waves in partially ice-covered water are generated in the laboratory. • Internal solitary wave induced currents can transport the ice horizontally. • In the laboratory experiments, dissipation of turbulent kinetic energy under the ice is comparable to that at the wave density interface.

Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences

Volume 2: Symposia, Parts A, B, and C, 2003

The dynamics of the break-up of curved jets produced by the prilling process were studied. The ef... more The dynamics of the break-up of curved jets produced by the prilling process were studied. The effects of liquid dynamic viscosity, rotation rate and orifice size upon the surface tension driven instabilities were investigated. Liquid dynamic viscosity was varied by using ...

Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 2014

Steady solitary and generalized solitary waves of a two-fluid problem where the upper layer is un... more Steady solitary and generalized solitary waves of a two-fluid problem where the upper layer is under a flexible elastic sheet are considered as a model for internal waves under an ice-covered ocean. The fluid consists of two layers of constant densities, separated by an interface. The elastic sheet resists bending forces and is mathematically described by a fully nonlinear thin shell model. Fully localized solitary waves are computed via a boundary integral method. Progression along the various branches of solutions shows that barotropic (i.e. surface modes) wave-packet solitary wave branches end with the free surface approaching the interface. On the other hand, the limiting configurations of long baroclinic (i.e. internal) solitary waves are characterized by an infinite broadening in the horizontal direction. Baroclinic wave-packet modes also exist for a large range of amplitudes and generalized solitary waves are computed in a case of a long internal mode in resonance with surface modes. In contrast to the pure gravity case (i.e without an elastic cover), these generalized solitary waves exhibit new Wilton-ripple-like periodic trains in the far field.

Journal of Fluid Mechanics, 2012

Journal of Fluid Mechanics, 2014

Journal of Engineering Mathematics, 2010

The evolution in time of three-dimensional gravity and gravity–capillary free-surface flows gener... more The evolution in time of three-dimensional gravity and gravity–capillary free-surface flows generated by a moving pressure distribution is considered. Solutions of the fully nonlinear equations in deep water are calculated by boundary-integral-equation methods and marching in time. Comparisons between unsteady and steady solutions are discussed.

IMA Journal of Applied Mathematics, 2013

ABSTRACT The deformation of a circular, inextensible elastic cell is examined when the cell is pl... more ABSTRACT The deformation of a circular, inextensible elastic cell is examined when the cell is placed into two different background potential flows: a uniform stream and a circulatory flow induced by a point vortex located inside the cell. In a circulatory flow a cell may deform into a mode m shape with m-fold rotational symmetry. In a uniform stream, shapes with two-fold rotational symmetry tend to be selected. In a weak stream a cell deforms linearly into an ellipse with either its major or its minor axis aligned with the oncoming flow. This marks an interesting difference with a bubble with constant surface tension in a uniform stream, which can only deform into a mode 2 shape with its major axis perpendicular to the stream (Vanden-Broeck & Keller, 1980b). In general, as the strength of the uniform stream is increased from zero, solutions emerge continuously from the cell configurations in quiescent fluid found by Flaherty et al. (1972). A richly populated solution space is described with multiple solution branches which either terminate when a cell reaches a state with a point of self-contact or loop round to continuously connect cell states which exist under identical conditions in the absence of flow.

IMA Journal of Applied Mathematics, 2012

European Journal of Mechanics - B/Fluids, 2014

Applied Mathematical Modelling, 2009

ABSTRACT We examine a spiralling slender viscous jet emerging from a rapidly rotating orifice, ex... more ABSTRACT We examine a spiralling slender viscous jet emerging from a rapidly rotating orifice, extending Wallwork et al. [I.M. Wallwork, S.P. Decent, A.C. King, R.M.S.M. Schulkes, The trajectory and stability of a spiralling liquid jet. Part 1. Inviscid theory, J. Fluid Mech. 459 (2002) 43–65] by incorporating viscosity. The effects of viscosity on the trajectory of the jet and its linear instability are determined using a mixture of computational and asymptotic methods, and verified using experiments. A non-monotonic relationship between break-up length and rotation rate is demonstrated with the trend varying with viscosity. The sizes of the droplets produced by this instability are determined by considering the most unstable wave mode. It is also found that there is a non-monotonic relationship between droplet size and viscosity. Satellite droplet formation is also considered by analysing very short wavelength modes. The effects of long wavelength modes are examined, and a wave which propagates down the trajectory of the jet is identified for the highly viscous case. A comparison between theoretical and experimental results is made, with favourable agreement. In particular, a quantitative comparison is made between droplet sizes predicted from the theory with experimental observations, with encouraging agreement obtained. Four different types of break-up are identified in our experiments. The experimentally observed break-up mechanisms are discussed in light of our theory.

... [4] studied the forces due to ice loads on wind turbines in Denmark. ... introduce Cartesian ... more ... [4] studied the forces due to ice loads on wind turbines in Denmark. ... introduce Cartesian coordinates with the x-axis being along the ice sheet at rest and the y-axis directed vertically ... For the case of free-surface waves reflected by a vertical wall with no ice sheet, there is no need ...

Journal of Fluid Mechanics, 2011

Journal of Fluid Mechanics, 2007

A configuration consisting of two superposed fluids bounded above by a free surface is considered... more A configuration consisting of two superposed fluids bounded above by a free surface is considered. Steady three-dimensional potential solutions generated by a moving pressure distribution are computed. The pressure can be applied either on the interface or on the free surface. Solutions of the fully nonlinear equations are calculated by boundary-integral equation methods. The results generalize previous linear and weakly nonlinear results. Fully localized gravity-capillary interfacial solitary waves are also computed, when the free surface is replaced by a rigid lid.

J. Nonlin. Sci. Appl.

Steady two-dimensional free-surface flows subjected to multiple localised pressure distributions ... more Steady two-dimensional free-surface flows subjected to multiple localised pressure distributions are considered. The fluid is bounded below by a rigid bottom, and above by a free-surface, and is assumed to be inviscid and incompressible. The flow is assumed irrotational, and the effects of both gravity and surface tension are taken into account. Forced solitary wave solutions are found numerically, using boundary integral equation techniques, based on Cauchy integral formula. The integrodifferential equations are solved iteratively by Newton's method. The behaviour of the forced waves is determined by the Froude number, the Bond number, and the coefficients of the pressure forcings. Multiple families of solutions are found to exist for particular values of the Froude number; perturbations from a uniform stream, and perturbations from pure solitary waves. Elevation waves are only obtained in the case of a negatively forced pressure distribution.

J. Fluid Mech., 2011

Nonlinear travelling waves on a two-dimensional inviscid fluid sheet are investigated when the sh... more Nonlinear travelling waves on a two-dimensional inviscid fluid sheet are investigated when the sheet is bounded above and below by two thin elastic plates. Symmetric and antisymmetric solution branches are identified, together with a pair of bifurcation branches. It is shown that far along the branches the solutions approach limiting configurations that correspond to static solutions valid in the absence of fluid forcing.